I was running Elasticsearch and Kibana in a Ubuntu based docker container and I was able to reproduce similar case. I used elasticdump to export and import the data /1/. The imported dashboard was for two indices called topbeat-* and statsd-*. The importing works if the indices are already created when the import is done. If the import is made after the .kibana is yellow/green and it is the only index, the importing /1/ seem to break the discover tab in Kibana so that it does not load anymore. I did not see any relevant logs with default settings in the KIbana4 logs with the exception of timeouts /2/
The behavior is similar if manual import is made if for example only one of the indices is there. In that case the import is not done for the visualizations that are for the index that is not there.
The use case is to deploy a container with predefined setting for analytics. The Kibana version was 4.5.0 and Elasticsearch 2.3.2. Browser was latest Chrome.
/1/
npm install elasticdump
elasticdump --input=http://localhost:9200/.kibana --output=$ --type=data --searchBody='{"filter": { "or": [ {"type": {"value": "dashboard"}}, {"type" : {"value":"visualization"}}] }}' > kibana-exported.json
elasticdump --input=/kibana-exported.json --output=http://localhost:9200/.kibana --type=data
/2/
{"type":"response","@timestamp":"2016-05-27T10:55:31+00:00","tags":[],"pid":235,"method":"post","statusCode":201,"req":{"url":"/elasticsearch/.kibana/index-pattern/topbeat-?op_type=create","method":"post","headers":{"host":"app-kibana.env","content-length":"50","accept":"application/json, text/plain, /","origin":"https://app-kibana.env","kbn-version":"4.5.0","user-agent":"Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/50.0.2661.102 Safari/537.36","content-type":"application/json;charset=UTF-8","referer":"https://app-kibana.env/app/kibana","accept-encoding":"gzip, deflate, br","accept-language":"en-US,en;q=0.8"},"remoteAddress":"x.x.x.x","userAgent":"x.x.x.x","referer":"https://app-kibana.env/app/kibana"},"res":{"statusCode":201,"responseTime":54,"contentLength":9},"message":"POST /elasticsearch/.kibana/index-pattern/topbeat-?op_type=create 201 54ms - 9.0B"}